A127738 Triangle read by rows: the matrix product A004736 * A127701 of two triangular matrices.

1, 3, 2, 5, 5, 3, 7, 8, 7, 4, 9, 11, 11, 9, 5, 11, 14, 15, 14, 11, 6, 13, 17, 19, 19, 17, 13, 7, 15, 20, 23, 24, 23, 20, 15, 8, 17, 23, 27, 29, 29, 27, 23, 17, 9, 19, 26, 31, 34, 35, 34, 31, 26, 19, 10

Offset: 1

Author

Gary W. Adamson, Jan 27 2007

Keywords

• nonn
• tabl
• easy

Comments

Left column = A028387: (1, 5, 11, 19, 29, 41, 55, ...).

Examples

			First few rows of the triangle:
   1;
   3,  2;
   5,  5,  3;
   7,  8,  7,  4;
   9, 11, 11,  9,  5;
  11, 14, 15, 14, 11,  6;
  13, 17, 19, 19, 17, 13,  7;
  ...
		

Crossrefs

Cf. A004736, A127701, A008778 (row sums), A028387.

Formula

T(n,k) = Sum_{j=k..n} A004736(n,j)*A127701(j,k). - R. J. Mathar, Aug 31 2022

T(n,k) = k+(k+1)*(n-k) = n+k*(n-k) = n +A094053(n,k) = A059036(n,k). - R. J. Mathar, Aug 31 2022